1Université de Bordeaux, Bordeaux, France 2University of Waterloo, Waterloo, Canada
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 489-494
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Marthe Bonamy; Michelle Delcourt; Richard Lang; Luke Postle; Marthe Bonamy; Michelle Delcourt; Richard Lang; Luke Postle. Asymptotically good local list edge colourings. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 489-494. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a20/
@article{AMUC_2019_88_3_a20,
author = {Marthe Bonamy and Michelle Delcourt and Richard Lang and Luke Postle and Marthe Bonamy and Michelle Delcourt and Richard Lang and Luke Postle},
title = { Asymptotically good local list edge colourings},
journal = {Acta mathematica Universitatis Comenianae},
pages = {489--494},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a20/}
}
TY - JOUR
AU - Marthe Bonamy
AU - Michelle Delcourt
AU - Richard Lang
AU - Luke Postle
AU - Marthe Bonamy
AU - Michelle Delcourt
AU - Richard Lang
AU - Luke Postle
TI - Asymptotically good local list edge colourings
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 489
EP - 494
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a20/
ID - AMUC_2019_88_3_a20
ER -
%0 Journal Article
%A Marthe Bonamy
%A Michelle Delcourt
%A Richard Lang
%A Luke Postle
%A Marthe Bonamy
%A Michelle Delcourt
%A Richard Lang
%A Luke Postle
%T Asymptotically good local list edge colourings
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 489-494
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a20/
%F AMUC_2019_88_3_a20
We study list edge colourings under local conditions. Our main result is an analogue of Kahn's theorem in this setting. More precisely, we show that, for a simple graph $G$ with sufficiently large maximum degree $\Delta$ and minimum degree $\delta \geq \ln^{25} \Delta$, the following holds. Suppose that lists of colours $L(e)$ are assigned to the edges of $G$, such that, for each edge $e=uv$, $$|L(e)| \geq (1+o(1)) \cdot \max\left\{\deg(u),\deg(v)\right\}.$$ Then there is an $L$-edge-colouring of $G$. We also provide extensions of this result for hypergraphs and correspondence colourings, a generalization of list colouring.
